# Is there a constant power supply?

A voltage source is a device that produces constant voltage, but allows amperage and power to vary, in accordance with the laws of electricity. A current source is a device that produces constant current, allowing voltage and power to vary.

Is there a constant power source – i.e., a device whose output power never varies? No matter the nature of what it is connected to, its voltage and amperage would be adjusted to provide constant power. (Its behavior would be undefined for both open and broken circuits.)

-
Nature of load?Linear or Non-Linear?How load can vary?How you plan to use? – Gopi Apr 1 '14 at 15:44
Why such kind questions for very fundamental things like sources etc, placed very frequent and they are so popular? – GR Tech Apr 1 '14 at 20:07
Are you asking if there is an 'ideal' power source, in circuit analysis. Is question you're asking, 'Since we have ideal voltage sources, and ideal current sources, can we have ideal power sources?' – JFA Apr 2 '14 at 6:35
A full answer would note both theoretical and practical examples, if they exist. – PyRulez Apr 2 '14 at 13:24

Yes, it's very easy to construct a constant-power supply.

Take, for example, an ordinary switchmode boost converter.

simulate this circuit – Schematic created using CircuitLab

Let's assume it is operating in discontinuous mode and does not have synchronous rectification (i.e., just a diode). If the switch is operated with a fixed duty cycle (i.e., no feedback), it puts a fixed amount of energy into the inductor each time it is closed. The amount of energy depends only on the input voltage, the inductance and the on-time. That energy gets dumped into the load when the switch opens.

Constant energy per cycle × constant number of cycles per second = constant energy per second = constant power.

Regardless of the resistance of the load, the voltage and current levels will adjust themselves to match that value of power.

In terms of practical limits, if the output of this supply is shorted, then the current will be limited by the resistance of the internal components (the inductor and diode). If the output is left open, the voltage will be limited by the distributed capacitance of the components — the inductor will "ring" with some high voltage at the self-resonant frequency.

-
The reverse of this is in common use as "maximum power point tracker" for solar cells: for a given output voltage, vary the input voltage/current point for maximum power transfer from the cells. – pjc50 Apr 1 '14 at 15:02
@pjc50: Yes, a switchmode converter can be used as an adjustable load for a solar panel, and along with suitable voltage and current sensors, a feedback loop that performs MPPT can be constructed. But I don't follow how this is in any sense the "reverse" of what I'm talking about in my answer. The whole point of MPPT is that the actual value of maximum power varies. – Dave Tweed Apr 1 '14 at 15:16
@tuskiomi: No. If you want to regulate the power, you do not get to choose either the voltage or the current. The load resistance sets both of those values: $V = \sqrt{P \cdot R}$ and $I = \sqrt{\frac{P}{R}}$ – Dave Tweed Jan 1 at 0:49
@tuskiomi: Ah, in that case, yes, there is a formula. The input energy per switching cycle $E = \frac{1}{2}I_{peak}^2\cdot L$. The peak current is a function of the on time, the inductance and the input voltage: $I_{peak} = \frac{V_{in} t_{on}}{L}$. The power is simply the energy per cycle multiplied by the switching frequency: $P = E \cdot f_{SW}$. You can combine these equations to get an overall equation for power. – Dave Tweed Jan 1 at 0:58
This is not 100 % correct because of a common fallacy. The output power of this circuit does depend on the output voltage. The peak inductor current is V.t/L, but the energy delivered is not just 1/2.L.I^2 -- additional energy is delivered by VIN during the discharge of the inductor.. Discharge time is Toff=L.Ipeak/(VOUT-VIN), and energy delivered to output is Vout.Ipeak.Toff/2 – jp314 Jan 1 at 1:29

A true "constant power" supply would output infinite current into a short, and produce infinite voltage across an open-circuit; in practice, any supply is going to have a limit to the voltage and current it will produce, regardless of output power.

Between those limits, many switching supplies in the 60-watt range will in fact behave very much like constant-power supplies when the current is high enough that at full voltage they would need to output more power than they are capable of, but low enough not to trigger a current-limiting circuit. From what I can tell, it's common for a family of supplies of different voltages to have the same maximum current, and differ only in the maximum voltage they will produce. If one makes a log-log plot of the output voltage-vs-current curves, the supplies in a family will share the same diagonal line for output power, and will share the same vertical line for maximum current; the only difference will be the height of a horizontal line which limits maximum voltage.

Note that one must check the data sheets of any supply one might wish to use in such fashion, to make certain one is clear about what aspects of operation are or are not specified.

-

Is there a constant power source

Yes, this is possible to do. I actually did it once many years ago as a demonstration. Voltage and current can be directly measured and directly controlled with analog electronics, so response can be good. There is no good way to directly control power, nor to measure power.

Power is the product of voltage and current, so one way is to measure those two, then perform a multiply to get a signal proportional to power. This is difficult in analog electronics. When I did this a long time ago, I used a digital processor to compute power from measured voltage and current, then tweak the output up and down accordingly. This was a long time ago and I was using a desktop computer over a IEEE-488 interface to control the electronics. It did about 10 loop iterations per second, which was enough for the purpose of demonstrating what I wanted to demonstrate.

Today, switching power supplies are routinely controlled by small embedded processors that measure voltage and sometimes current every switching pulse. Digital multiplies can be as short as single cycles, so doing closed loop power control is much more feasable today. However, there is very little use for this. I've designed a bunch of constant-voltage switching power supplies and a few constant-current switching power supplies, but never a constant-power supply. That's not because it couldn't be reasonably done today, but because I haven't come accross a use for one.

that is, a device who's output never varies?

This is a nonsensical question. What output? Voltage? Current? Power? Something else? We do engineering here, not hand waving.

There also seems to be some confusion about what a power supply can and can't control. Think of even the simple case where the load (what is connected to the power supply beyond the control of the supply) can be any resistor. The voltage, current, and resistance are related by Ohm's law:

Current = Voltage / Resistance

or in common units:

A = V / Ω

Notice how there are only two degrees of freedom in this relationship. If you define any two, there is no choice left about the third. Since the load always gets one degree of freedom, the power supply only gets one degree of freedom too.

You can rearrange this various ways. For a constant voltage supply, the supply choses voltage, the load choses resistance, and the current comes out to what it comes out to. Or, the load choses current and the apparent resistance seen by the supply comes out to what it comes out to.

Power is voltage times current. With this and Ohms law, you can get:

Power = Voltage2 / Resistance

Again, only two degrees of freedom. If the power supply regulates power and the load choses the resistance, then the voltage comes out to what it comes out to.

You can't cheat basic physics.

-
Completely agree.How can we construct constant power supply if load can be linear or non linear? Load can vary?Unless the model of load is known, difficult to make it. – Gopi Apr 1 '14 at 15:41
Oh sorry, miss wording. I meant output power never varies. – PyRulez Apr 1 '14 at 21:13

Yes, but more pratically, these devices are called electronic loads. They can be set to draw a constant current or a constant POWER from a power supply. They are useful for power supply testing, battery testing, and solar testing.

Constant power supplies are less common, but one practical application is keeping an LCD that is used in outside in the cold warm enough so that that moving images do not smear. The heating element of the LCD is a thin sheet of translucent material called Indium Tin Oxide. Or there may a thin wire in the LCD Screen. In either case, the resistance of the heater varies considerably with temperature. If you fed the heater with a constant current or constant voltage, the power would be a strong function of ambient temperature.

However, we wish to have relatively constant power, so a constant power supply is used.

-

A voltage source is easy enough except when you think about short circuits - infinite current is taken and for this reason, voltage sources, in the strictest sense don't exist.

Current sources have the same problem on an open circuit - how can current be pumped into space without the current source exerting infinite voltages to force a constant current.

Power sources are contrived from voltage and current sources and can exist on paper but, just like real current and voltage sources, don't match up to theoretical expectations.

-

A flyback voltage converter with fixed oscillation frequency and fixed duty cycle will produce constant power as long as the load doesn't vary too quickly.

When the load varies over time, the output filter prevents the converter from adjusting the supplied power quickly, which may or may not be a problem in your case.

-

There are commercially available power supplies that have a constant power mode. An example is the Sorensen SG Series.

-

There is another way of producing an approximate constant power source, which is useful if your load changes with temperature. If you put a series resistor of the same value as the load then the power evens out. One way of looking at it is that if the series resistor is zero then the load is driven by a constant voltage. If the series resistor is infinite then the load is driven by constant current. dP/dR = 0 when Rs = Rl. Of course this is not an eco friendly way of doing it. Roger Williamson

-

another use for a low power constant power source could be in measuring gas flow with a single nichrome wire. Push constant power through the wire; a constant amount of heat is generated, the wire heats up, and the wire resistance increases. You can calculate wire resistance from voltage/current and thus, can know the wire temperature. In still gas, the temperature gain above ambient can be so determined.

gas flowing past the wire removes heat from the wire at a greater rate than at zero velocity, and amount of heat loss is proportional to gas speed.

-
This doesn't really seem to address the original question, which is whether such a device exists rather than possible uses for one. – PeterJ Aug 21 '14 at 5:33